After a hurricane, a homeowner examine tree on hi property for damage. He think a 21-ft palm tree i leaning lightly from it original vertical poition. From a point 23 ft away, he meaure the angle of elevation to the top of the palm tree a 46°

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16-12-2022
Mathematics

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After a hurricane, a homeowner examine tree on hi property for damage. He think a 21-ft palm tree i leaning lightly from it original vertical poition. From a point 23 ft away, he meaure the angle of elevation to the top of the palm tree a 46°

Answer :

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GopalBarman GopalBarman · Answer 1 · 2022-12-23T07:43:07-05:00

After a hurricane, a homeowner examine tree on hi property for damage. He think a 21-ft palm tree i leaning lightly from it original vertical position. From a point 23 ft away, he measure the angle of elevation to the top of the palm tree a 46°, so the leaning angle becomes: 84.01°

What is angle of elevation?

"Rise over Run," which equals the rise (the change in vertical distance) divided by the run, is a simple formula for calculating the change in elevation as a decimal (the change in horizontal distance).

tan θ = perpendicular / base

or, tan 46° = perpendicular / 23

or, 1.04 = perpendicular / 23

or, perpendicular distance = 23.81 ft > 21 ft.

So, the palm tree is leaning.

Now, how much leaning the palm tree is:

After leaning the angle becomes: (90° - 46°) = 44°

perpendicular distance / sin x = palm tree distance / sin 44°

or, 23.81 / sin x = 21 / 0.695

or, sin x = 23.81 × 0.695 / 21

or, sin x = 0.788

or, x = 51.99°

Again,

51.99° + 44° + leaning angle = 180°

or, leaning angle = 84.01°

To know more about angle of elevation refer to:

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The complete question is as follows:

After a hurricane, a homeowner examines trees on his property for damage. He thinks a 21-ft palm tree is leaning slightly from its original vertical position. From a point 23 ft away, he measures the angle of elevation to the top of the palm tree as 46°. Is the palm tree leaning? If so, by how many degrees from the vertical? Round to the nearest tenth of a degree. The palm tree is not leaning. The palm tree is leaning. The palm tree is leaning by degrees from the vertical.